148 CHAPTER 4. UNDERSTANDING FORWARD EXCHANGE RATES FOR CURRENCY
currency is under pressure, and the result often is an appreciation of the spot value.
How can increasing the interest rate, a sign of weakness, strengthen the currency?
The relation to watch is, familiarly,St =CEQt(S ̃T)(1 +rt,T∗ )
1 +rt,T. (4.27)
We also need to be clear about what is changing, here, and what is held constant.
Let’s use an example to guide our thoughts.
Example 4.18
Assume that thecad(home currency) andgbprisk-free interest rates,rt,Tandr∗t,T,
are both equal to 5 percentp.a.Then, from Equation [4.27], initially no change in
Sis expected, after risk adjustments: the spot rate is set equal to the certainty
equivalent future value. Now assume that bad news about the British (foreign)
economy suddenly leads to a downward revision of the expected next-year spot
rate from, say,cad/gbp2 to 1.9. From Equation [4.27], if interest rates remain
unchanged, the current spot rate would immediately react by dropping from 2 to
1.9, too. Exchange rates, like any other financial price, anticipate the future.
Now if the Bank of England does not like this drop in the value of thegbp, it
can prop up the current exchange rate by increasing the British interest rate. To
do this, theukinterest rate will need to be increased from 5 percent to over 10.5
percent, so thatStequalscad/gbp2 even though CEQt(S ̃T) equals 1.9:
1. 9 × 1. 10526
1. 05= 2. (4.28)
Thus, the higherukinterest rate does strengthen the currentgbpspot rate, all else
being equal.
But this still means that the currency is weak, in the sense that thegbpis still
expected to drop towards 1.9, after risk-adjustment, in the future. Actually, in this
story the pound strengthens now so that it can become weak afterwards. So there
is no contradiction, since “strengthening” has to do with the immediate spot rate
(which perks up as soon as theukinterest rate is raised, holding constant theceq),
while “weakening” refers to the expected movements in the future.
A second comment is that, in the example, the interest-rate hike merely post-
pones the fall of the pound to a risk-adjusted 1.9. In this respect, however, this
partial analysis may be incomplete, because a change in interest rates may also af-
fect expectations. For instance, if the market believes that an increase in the British
interest rate also heralds a stricter monetary policy, this would increase the expected
future spot rate, and reinforce the effect of the higher foreign interest rate. Thus,
the BoE would get away with a lower rise in theukinterest rate than in the first
version of the story.
Of course, if expectations change in the opposite direction, the current spot rate
may decrease even when the foreign interest rate is increased. For example, if the